I am recently involved in two projects. Both have tight deadlines. One project manager hopes that I can finish his tasks by the early next week. Another project manager hopes that I can finish her tasks this week. I estimate that my time this week is not enough to finish all of the tasks they expected me to finish. How should I communicate with these two project managers?
What is the nature of the tasks? Do you work on 1 or more at a time or finish one and move on?
If you you have a scheduler or resource manager talk to them. If neither project manager is your boss talk to your boss. Things will hopefully go fine with the project managers but if not your manager will at least have a heads up.
I would write an email with the tasks and projections for when you expect to finish. CC your scheduler / resource manager / boss.
Send an email to both immediately advising them of the situation.
As I used to tell my reports, "When you address troubles before a deadline, it's a concern, after a deadline it's an excuse".
Be able to articulate your difficulties and demonstrate why there is not enough time to get both done, then they'll either have to hammer it out themselves, or escalate it to their manager(s) to have a management decision made.
Just make sure you are covered and can document the fact that you are indeed overloaded.
A pint cannot hold a gallon, when it is holding a pint, it is already doing the very best it can.